1.1 Objectives

1.2 Introduction

2.1 3 General Strategies

• Important: There is considerable controversy and conflicting ideas in this area, as to 'what should we do' - take non-parametric class for more fun!

• We need a way to address assumption violations when they occur (well mostly - see Do Nothing!)
  • As mentioned before, the main risk of assumption violations, is that they reduce power and raise Type II error rate
  • Since we are coming into most studies with a hypothesis of differences existing, we want to plan an analysis that has the sufficient power to detect that hypothesized difference
• We have 3 strategies for approaching assumption violations:
  • Do Nothing!
  • [Correct for Violations in Data]
  • Use Non-parametric Tests

2.2 Do Nothing!

• Without going into too much detail, we are concerned with how robust a test is, or how resilient a test is to assumption violations, and how well it works under less-than-ideal circumstances

• Some researcher’s hold that many commonly used tests, i.e., t-tests are reasonably robust at baseline to assumption violations

  • This becomes even more true at large \(n\) size (See discussion in [Sample Size] section])
  • However, when samples are small or the groups being compared are unequal - this route cannot be recommended

2.3 Correct for Violations in Data (Transformation)

• There are several options for selectively transforming and or trimming our data to correct for certain patterns of skewness, kurtosis, or outliers
  • However, be aware these are not panaceas - they come with their own issues

Transformations

• Making mathematical variable transformations is largely used to address the [Normality Assumption], but maybe indirectly solve other issues as well

• The exact transformation is dependent on the type of problem, specifically the skew:

  • Positive/right skew: Logarithmic (Severe) or Square Root (Moderate)
  • Negative/left skew: Reflect and Logarithmic (Severe) or Reflect and Square Root (Moderate)

• Advantages:

  • Makes use of all available data
  • Allows for use of a traditional well-known technique.

• Disadvantages:

  • Interpretability can be questionable
  • Fixing one assumption violation can create others

Trimming

• Another option, particularly useful for negatively kurtotic (platykurtic) distributions (relatively flat distributions with an unusual number of observations in the tails) is to use variable trimming.

• A trimmed sample is a sample where a fixed percentage of extreme values is removed from each tail.

  • Of course, if you are comparing groups, you would want to trim the same percentage from the tails of both groups to be fair.
  • 0.20 from each tail is the most common amount to trim

• Another related option is using winsorizing

  • A Winsorized sample replaces the trimmed values by the most extreme value remaining in each tail.
  • Note: degrees of freedom for a test on a trimmed or Winsorized sample must be adjusted for the data trimming. For both, you would subtract your total N by the number of trimmed cases to get a new value for N. (We do this even for Winsorized samples b/c the added values are really pseudovalues.)

• Advantages:

  • Allows for use of a traditional well-known technique.
  • Interpretability of variable remains intact

• Disadvantages:

  • Loss of information - what if those outliers were an important part of the phenomenon

2.4 Use Non-parametric Tests

3.1 Recap

3.2 Lecture Check-in

• Make sure to complete any lecture check-in tasks associated with this lecture!

Module 3 Lecture - Transformations and Non-parametric Comparisons for Two Groups || Analysis of Variance